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Game Theory: Assurance Game (aka why people arrive late)

The Prisoner’s Dilemma game assumes that there is a conflict between self-interest and the benefits achieved through mutual cooperation.

The Assurance game, also known as the stag hunt (see below), however, models interactions where mutual cooperation is the best possible outcome, but where cooperation may involve an element of risk. In such situations both players need assurance or trust to risk cooperation.

It’s customary for people to arrive socially late to parties.

If you invite your mates over for 7, often they won’t arrive until 730 or even 8. Clearly this is a suboptimal outcome: arriving late means that people spend less time together and punishes punctual people.

The reason people arrive socially late is because that is a safer decision than showing up on time and risking being the only one there. Let’s take a look at the Assurance Game and explain why showing up late holds less risk.

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First lets explain the assurance game.

Two people face the choice of going to a lecture (C) or staying at home (D). Both regard going to the lecture together to be the best alternative; both consider staying at home together to be the next best; and each considers going to the lecture without the other worst. The Assurance game differs from the Prisoner’s Dilemma in that the (C, C) outcome is a Nash equilibrium—neither player can do better than to cooperate if the other chooses to cooperate. For player I, C is the best reply to player II’s C, and for player II, C is the best reply to player I’s C. But there is another Nash equilibrium at (D, D), where strategies are also best replies to each other.

Furthermore, the Nash equilibrium that both prefer (that is, mutual cooperation) involves greater risk because each has to risk the worst possible payoff if they choose to cooperate and the co-player defects. This game models situations in which both participants are better off working together, but if either defects from a cooperative mode of interaction it is best for the other to do likewise because unilateral cooperation yields the worst possible payoff to the cooperator and does not bring much benefit to the co-player.

Trust and assurance are crucial in promoting cooperation in the Assurance game. If each player can be relatively confident that the other will cooperate, then mutual cooperation is a likely outcome. As in the case of the Prisoner’s Dilemma game, the outcome will be influenced by whether the interaction is a ‘‘one-off’’ or is in the context of a series of repeated interactions.

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So, back to the party. Should you show up on time or socially late to a party?

If you show up socially late, then you are guaranteed a payoff. If you show up on time your payoff depends on what other people have done. Showing up late mean

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The French philosopher, Jean Jacques Rousseau, presented another example of the assurance game. Two hunters can either jointly hunt a stag (an adult deer and rather large meal) or individually hunt a rabbit (tasty, but substantially less filling). Hunting stags is quite challenging and requires mutual cooperation. If either hunts a stag alone, the chance of success is minimal. Hunting stags is most beneficial for society but requires a lot of trust among its members.